German Patent No. 197 00 935 A1 discloses a hydrostatic actuator of this type in the form of a hydrostatic clutch actuator. In accordance with this document, a piston of a master cylinder is driven by an electric motor and the rotary movement of the electric motor is converted into an axial movement by a gearing mechanism in the form of a worm drive. The piston is driven by an eccentric pin arranged on the worm gear.